Question

If the third term of a G.P. is $2$, then the product of first $5$ terms is

• A. $5^2$
• B. $2^5$
• C. $10$
• D. $15$

Answer 1

The correct option is B $2^5$

It is given that the third term of the G.P is $2$.

We know that the general term of an geometric progression with first term $a$ and common ratio $r$ is $T_n=a{r}^{n-1}$, therefore,

$T_3=a{r}^{3-1}\Rightarrow 2=a{r}^2......\left(1\right)$

Now, consider the product of first five terms that is:

$a\times ar\times a{r}^2\times a{r}^3\times a{r}^4=a^2{r}^{10}=(a{r}^2{)}^5=(2{)}^5\left(using\right(1\left)\right)=32$

Hence the product of first $5$ terms is $32$.